The recommended reference client for using Matrix is called Element and is available for various platforms:
The easiest way is to open the Element Web application directly in a modern browser (e.g. Mozilla Firefox).
More recommendable than using a browser tab is the installation of the program Element on your own computer. Here you can keep the overview independently of the browser (however, you should also take care of the updates of the program).
On the road, access to Matrix is possible, for example, via smartphone with the help of the mobile Element Apps.
Downloads for: iOS (iPhone/iPad)